We read breathless analysis a week or so ago that the best shot in basketball is a three-pointer and it may be analytically correct.

As lone as someone one makes one every now and then.

After throwing up a 4-17 furball from distance on Wednesday night – that’s an atrocious percentage by any standards – Toronto is now shooting, as a team, 22.8 per cent in its last five games (26-for-114) and 28.6 in its past 10 (59-for-206).

That’s not efficient and no one can possible tell me that it is so if they are going to believe in that “take lots” theories, they might want to mention to the GM that they need people proficient from beyond the arc. Heck, they’d probably settle for marginally good rather than proficient because, right now, they suck.

It is true that the Raptors are not very good at making three point shots and could use some help in that department. But does that mean that the team should stop taking three-point shots?

In their past 10 games the Raptors are indeed making only 28.6% of their three-point shots. But because three-point shots are worth an extra point when they go in, it’s not fair to use simple field-goal percentage to measure three-point accuracy. That’s where Effective Field Goal percentage (eFG%) comes in handy. eFG% is calculated using the following formula:

eFG% = [FGM + 0.5 x 3PM] / FGA

Using the formula, we can see if going 59-206 from three hurts the Raptors:

Type of Shot

Made

Attempted

FG%

eFG%

3PT

59

206

28.6%

43.0%

2PT

305

605

50.4%

50.4%

Field Goal

364

811

44.9%

48.5%

As you can see, making 59 of 206 three-point shots is equivalent to hitting 88.5 of 206 (43%) two-point shots. At the same time, the Raptors were shooting 50.4% on their two-point shots. So yes, the Raptors’ bad three-point shooting hurt them. But notice how relatively small the impact was? The eFG% drops from 50.4% (when we only count two-point shots) to 48.5% (when we also count three-point shots). So it’s a relatively small drop. Now don’t get me wrong: shooting efficiency is the single most important factor when it comes to basketball productivity. But watch how quickly eFG% increases when you start making more three-point shots:

Type of Shot

Made

Attempted

FG%

eFG%

3PT

59

206

28.6%

43.0%

3PT

60

206

29.1%

43.7%

3PT

61

206

29.6%

44.4%

3PT

62

206

30.1%

45.1%

3PT

63

206

30.6%

45.9%

3PT

64

206

31.1%

46.6%

3PT

65

206

31.6%

47.3%

3PT

66

206

32.0%

48.1%

3PT

67

206

32.5%

48.8%

3PT

68

206

33.0%

49.5%

3PT

69

206

33.5%

50.2%

Had the Raptors made a mere ten more three pointers, they’d have broken even. While this proves how bad their shooting has been, it also proves how important three pointers are. And it’s likely the Raptors have simply been on a cold streak, in the last 10 years only 38 of 296 teams have failed to hit the required mark from three that would have kept the Raptors “good from three”.

Let’s even follow up on this analysis for the whole league. Are there any teams hurting their efficiency with their three point shooting? It turns out only two teams fit this mold: the Denver Nuggets and the Minnesota Timberwolves!

Denver shoots 34% from the arc, which is ranked 24th in the league. Their real problem is they are efficient from two. They shoot 51.4% from two point range, which is good for fourth in the league. Their three point shooting isn’t actually hurting them (although, Dre would love for it to improve!), it’s just not as good as their two point shooting.

Minnesota is another story. They cannot hit from deep. At 30%, they are the worst team from deep. It doesn’t help that Kevin Love has missed over fifty games this season.

The Raptors have been hurting themselves from deep during the recent stretch. Over the season though, their three point shooting has helped. Unless you are a team crippled by injuries like the Wolves, it is simply bad business to stop shooting threes because of a cold streak. Three pointers are crucial to the modern game. Teams are still catching on, so Doug Smith’s chatter might still be taken seriously. That said, the end message we have is simple: keep shooting from three, it’s worth it!

18 Responses to "Yes, three-point shots are that good"

Regression to the mean is the bane of the sports writer, because they like to take smalls amples and over extrapolate. I mean, those 500 words don’t write themselves! I’d say, though, as the WoW blog proves, there are more, and easier, words to be written AGAINST common wisdom than with it.

Still, just like GMs, writers are more worried about their job security than being correct.

I clicked the link and waded in … Doug Smith must hail from an era I can never hope to understand. A time when men possessed mental fortitude, wore shoes that you wear on your feet, drank on the job, never capitulated and it was the failing even further in arrears. A time of bromide quotas, rations on insight, and sentences composed with the aid of a dictionary and jarts.

I don’t even know what this means “That’s not efficient and no one can possible tell me that it is so if they are going to believe in that “take lots” theories, they might want to mention to the GM that they need people proficient from beyond the arc,” and I read Trainspotting.

Philippe Soupault, is that you? It’s me, Duck Tarsal. Just ride the zeppelin to the Macgillycuddy, we’ll meet at the marzipan.

Since you mention reversion to the mean, it’s worth pointing out that over a sample of 206, a variation of 10-15 is creeping toward the edge of reasonable confidence intervals. If they only hit 59 of their next 206, as well, it’s really time to start asking questions.

Something else to consider: If the Raptors are shooting historically low rates of 3-pointers, then we might start asking how good their 3-point shooting decisions have been. We know that there are smart 3-pointers – ones that are open and from the corners, or straight on, and not-so-smart 3-pointers are from the wings, but they’re shooting the same 62% of their 3 pointers from the wings both on the season, and the last 10 games.

That said, the Raptor’s recent eFG on the wing 3’s is 40% – well below their season eFG of 51% – and this seems to be where most of the change in performance is.

Basically, you could think of it this way: journalists don’t get paid to be sophisticated, they are paid to be entertaining. This is an obvious case of using limited data to make an off the cuff assumption. But it sells newspapers.

Also, poor three point shooting doesn’t prove much on a team like the Raptors. What were the other options on the court when the three was taken? Maybe these threes are being taken when better post defenders on the court.

What’s funny about the NBA is that the owners appear to be as dumb as the journalists. If Warren Buffet would buy an NBA team, buy up the Kenneth Farieds of the league(also a few great passers), he could win a few championships and sell the team at a profit.

I believe that 3 pointers are slightly overrated by wins produced. The reason for this is that players draw very few fouls when shooting from 3.

As we know getting to the line is a big part of what makes an offense efficient. From the Wins Produced regression we know you need to shoot slightly better than 50% for your shots to be considered efficient. When you take free throws into account, however, it’s clear that merely shooting 50% isn’t getting you ahead – with free throws, you need to be averaging closer to *55%* true shooting to be netting your team points.

Hitting 3’s at a 34% clip isn’t really helping your team. Sure, you’re gaining ‘wins’ from the shots going in, but you’re losing wins from getting to the line at a below average rate. You need to be hitting at around a 35% clip before you start netting your team wins after you take that into account.

It is a small difference, but small differences add up to real wins over the course of a season. You have to be careful about valuing a particular play on the court, because each play will have an effect on many different stats – and you can draw bad conclusions if you don’t take all of it into account.

Brandon and Charles,
Both right here. Yes, Wins Produced already includes free throws. That said, I do actually really want to know the foul percentage by rate. Eventually (and thanks to SportsVU data this is much closer to reality) the ideal formula would be – shot location including shooting percentage, foul percentage and offensive rebound %.

Wins Produced takes it all into account; the narratives do not. When you’re doing the regressions the math is indifferent to how you do the accounting of covariant terms, but it matters a lot when telling a story. If you don’t include all the covariant terms in your story, you could be leaving important pieces of the puzzle out without even knowing it.

What Charles is means, I think, is that this argument doesn’t accurately account for ‘free throw equity’ from drawing fouls. For example, lets consider the Raptors:

The Raptors have shot 168/205 free throws in the last 10 games (NBA.com). I know it’s a little crazy, but let’s assume, for the sake of discussion, that this represents 103 fouled 2-point shots, only 1 of which went in. Then we could say that instead of getting 610 points on 605 2-point shots, the Raptors got 778 points on 707 shots – corresponding to an efG of around 55%. For an equivalent points per 3-point shot, they’d have to have hit around 75 of the 206 3-point attempts they took. (Including free throw points does reduce the relative impact of 3-point shooting.)

When calculating wins produced per player or per team, the formulae have terms for hit and missed free throw attempts, but the analysis here doesn’t seem to account for them at all. (And, as far as I am aware, there’s no box score breakout for how fouls were drawn.)

I’m too lazy to look through the literature about it, but another concern is that Wins Produced seems like a model created to deal with longer intervals of play, so it may benefit from offsetting effects that average out. Splitting out and regrouping possessions into 2 and 3 point shots could eliminate that sort of averaging effect, and thus produce misleading results.

Have you considered looking at three point percentages when teams are trailing in points?

It looks like teams force more three point shots when they are losing to try to get themselves back into the game. In that situation, should teams consider taking higher percentage shots or continue shooting threes?

Devin – speaking of the Raptors, it would be great to get an analysis of the Calderon + Davis trade for Rudy Gay. I did a back-of-the-envelope and figured it had cost the Raptors 7 wins so far (including the fact that Casey seemed to be saying that Davis had earned his roster spot* over Bargnani before the trade), which meant competing for playoffs vs. out of playoffs. You could do it far better.

* I wonder if Colangelo is the anti-Billy Beane, and said ‘you’re going to play Davis over Bargnani – let me trade Davis so you have to play Bargnani instead’.

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